Space of modular forms of level 650, weight 2, and Character 650.m

• Label: 650.2.m
• Level: $650$
• Weight: $2$
• Character orbit: 650.m
• Rep. character: $\chi_{650}(101,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $44$
• Newform subspaces: $5$
• Sturm bound: $210$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.m (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(210\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(650, [\chi])\).

	Total	New	Old
Modular forms	236	44	192
Cusp forms	188	44	144
Eisenstein series	48	0	48

Trace form

44 * q + 22 * q^4 - 18 * q^9 + 12 * q^11 - 12 * q^13 + 8 * q^14 - 22 * q^16 - 24 * q^19 + 14 * q^26 - 24 * q^27 - 6 * q^29 + 60 * q^33 + 18 * q^36 + 12 * q^37 + 24 * q^38 + 4 * q^39 - 30 * q^41 + 12 * q^42 - 24 * q^46 + 22 * q^49 - 16 * q^51 - 48 * q^53 - 36 * q^54 + 4 * q^56 - 12 * q^58 + 12 * q^59 - 6 * q^61 - 24 * q^62 - 48 * q^63 - 44 * q^64 + 16 * q^66 - 24 * q^67 - 20 * q^69 - 24 * q^72 - 22 * q^74 - 24 * q^76 + 24 * q^77 - 12 * q^78 + 8 * q^79 + 2 * q^81 + 36 * q^84 - 24 * q^87 + 24 * q^89 + 20 * q^91 - 36 * q^93 - 12 * q^94 - 36 * q^97 + 48 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(650, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
650.2.m.a	$650$	$2$	650.m	13.e	$6$	$4$	$2$	$5.190$	\(\Q(\zeta_{12})\)	None					130.2.l.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(-1+\zeta_{12}+\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+\cdots\)
650.2.m.b	$650$	$2$	650.m	13.e	$6$	$8$	$4$	$5.190$	8.0.22581504.2	None		✓			650.2.m.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{7}q^{2}+(1-\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)
650.2.m.c	$650$	$2$	650.m	13.e	$6$	$8$	$4$	$5.190$	8.0.22581504.2	None					130.2.l.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{4}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
650.2.m.d	$650$	$2$	650.m	13.e	$6$	$8$	$4$	$5.190$	8.0.22581504.2	None		✓			650.2.m.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{7}q^{2}+(2-\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)
650.2.m.e	$650$	$2$	650.m	13.e	$6$	$16$	$8$	$5.190$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			✓		130.2.m.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{1}+\beta _{6})q^{2}-\beta _{5}q^{3}-\beta _{8}q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(650, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(650, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)